I always cook mine in a frying pan, but have had times when the skin sticks to the pan. Not sure how to prevent that.

Hot pan, a touch of oil, and most importantly, let the salmon sit for a moment or two before fussing with it. All to often cooks don't allow time for the pores in a pan to be filled with protein and develop a barrier between the food and the pan. Give time to let your food start to caramelize before you move it around.

I grilled some salmon last night , on the stove, in a grill pan....and it didnt stick, I lubed it well with some olive oil and put a wee bit of olive oil in the pan before i put the salmon in, but i noticed some thing really obvious as i was grilling my salmon.
If you put that salmon in the pan so that , how do i say this...???
If salmon breaks up it breaks up in a particular direction, if we were talking wood , i would say that it breaks up with the grain of the wood.
Put in the pan so that the grain of the salmon is perpendicular to the ribs on the pan. Then when you get ready to lift it out, go against the ribs of the pan and you will be able to lift it with out it sticking very much or breaking up.
I was able to peel the skin of the salmon i cooked last night as I cooked the skinless side. Just peeled right off with the spatula

Sometimes I put a little bit of olive oil in a nonstick skillet. Then I put a salmon fillet in the oiled hot skillet. I cook a few minutes on each side. You can season the fillet before putting it in the skillet. Sometimes I put some lemon dill sauce on the cooked salmon.

If you're going to fry salmon, you're better off frying steaks. Filets are better for baking. At least that's what I've found out through trial and error.

I like to season the steaks with ground black pepper and medium to coarse sea salt. I let the steak sit for an hour or so in the fridge after seasoning (just personal pref., it allows the salt to melt and penetrate the salmon).

I sear my salmon on high until the first side is a crunchy brown. Flip and put the pan and all in the oven at 350 for 5 to 8 minutes, depending on thickness of the steak. I sometimes lay the raw salmon on capers to cook. When you flip the salmon, the most of the capers will stick to the surface. The capers are particularly delicious and impart a wonderful flavor to the fish. I love the capers crisp texture too.